By the Auslander-Buchsbaum-Serre Theorem, a singular ring has infinite global dimension. A 'non-commutative resolution' is given by a module M whose ring of endomorphisms has finite global dimension. Intuitively, this replaces the idea of 'projective modules' with 'summands of M'. When R is a domain of characteristic p>0, one possible M to consider is the module of p^e roots.

In this talk, I will demonstrate that, for toric algebras, the module of p^e roots gives a non-commutative resolution, and show how the precise module structure of the endomorphism ring can be described combinatorially. This is joint work with Eleonore Faber and Karen E. Smith.

Speaker(s): Greg Muller (University of Michigan)